Physicists Detect the Undetectable: "Baby" Solitary Waves

BUFFALO, N.Y. – When University at Buffalo theorist
Surajit Sen published his prediction that solitary waves, tight
bundles of energy that travel without dispersing, could break into
smaller, "baby" or secondary solitary waves, experts in the field
acclaimed it as a fine piece of work.

They also felt that these waves might never be seen
experimentally.

But in a paper published this week in Physical Review Letters,
Sen and his co-authors report that they have done just that.

The new results contribute to a better understanding of how
energy propagates through strongly nonlinear systems, where nearly
every detail of the system matters and that make up many of the
systems of interest to scientists.

"A central theme behind the physics of any system is how its
particles share and transmit energy," explained Sen. "This work
goes to the heart of nonlinear systems because it provides insights
into how such systems propagate energy."

The current research also may overturn completely the generally
accepted idea that equilibrium states – or at least a similar
type of state – cannot easily occur in nonlinear systems.

"Solitary waves are, by definition, energy bundles, which do not
fall apart," Sen explained. "They are not supposed to be easily
breakable because they are energy bundles, so they generally travel
intact and don't transform."

Unfortunately, the magnitude of the baby solitary waves that Sen
predicted was much less than one percent of the energy carried by
the entire solitary wave, far below detectable experimental
limits.

"When we published our papers, I also didn't believe these
phenomena would be detectable," admitted Sen.

His predictions were based on a collision of two solitary
waves.

"My assumption was that when two solitary waves in a granular
system collide head-on, the physics is similar to bouncing a
solitary wave off an infinitely hard wall," he said.

But the experiment conducted at Universidad de Santiago by Sen's
co-authors in fact produced "baby" solitary waves that were as
large as 15 or 20 per cent of the energy propagated through the
entire system.

What allowed the team to produce such large secondary waves, and
therefore verify the predictions, was the decision by Francisco
Melo, Ph.D., professor of physics at the Universidad de Santiago,
to collide solitary waves traveling through a chain of 20 identical
stainless beads against a wall made of a soft material.

Melo, his post-doctoral researcher, Stephane Job (now an
assistant professor at Institute Superieur de Mecanique de Paris),
and UB undergraduate physics major Adam Sokolow, also a co-author,
embedded non-intrusive force sensors into one bead and the
reflecting wall.

The beads were bounced against the wall and the sensor then
recorded the amount of force with which the last bead hit the soft
wall.

"To observe large baby solitary waves, the idea is that by
introducing a large mismatch of mechanical properties at the wall,
the reflected solitary wave needs to adapt more dramatically, thus
producing such large baby solitary waves," explained Melo.

This set-up resulted in successfully amplifying the effect Sen
had predicted so greatly that it was experimentally verifiable.

"This work proves that these solitary waves, or energy bundles
can be made to 'leak,' in a sense, producing these secondary or
baby waves," said Sen.

Even more interestingly, he said, the work indicates that it may
be possible to control that leakage, potentially leading to a new
understanding of how a physical state akin to equilibrium may exist
in nonlinear systems.

"For physicists and mathematicians, systems in equilibrium are
like the ocean, they are in a tranquil, settled state," explained
Sen. "But when you talk about solitary waves propagating in a
system, you're as far away from a system in equilibrium as you can
be because these systems carry significant amounts of energy as
propagating energy bundles, sort of like a propagating shock
front.

"Our work shows that a system can propagate a huge pulse of
energy as in a shock wave, but if placed between two walls, the
original energy you gave to the system can get broken down," he
said. "Since that energy can end up being shared by all grains or
spheres in the system, there is some semblance of equilibrium
here."

The experiment also resulted in an unexpected finding about a
materials constant called the Youngs modulus – which
describes the ability to stretch or squeeze a material-- that is
usually more the concern of mechanical and materials engineers than
physicists, Sen said.

"Bouncing a solitary wave against a surface provides an accurate
and non-invasive way to measure the Youngs modulus of a surface,"
he explained.

UB undergraduate Adam Sokolow, who was awarded a UB
Undergraduate Research and Scholarly Award of Distinction for this
work, spent the summer of 2004 at the Universidad de Santiago,
acting as a bridge between the simulations performed by his UB
mentor, Surajit Sen, and the complex experimental work, which was
carefully controlled by post-doctoral researcher Job.

Sokolow's stay was funded by the Consortium of the Americas for
Interdisciplinary Science of the University of New Mexico, designed
to facilitate collaborations between scientists in New Mexico and
throughout the United States with those in Latin America.

The research was funded partly by the National Science
Foundation and by CONICYT, Chile's National Commission for
Technological and Scientific Research.

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